Question

the equilateral triangle AOB lie within the square ABCD.let us write the value of angle COD.

Answer 1

Answer

Given: The equilateral triangle AOB lies within the square ABCD. Let us write the value of ∠COD.

To find: ∠COD

As, ABCD is a square and all sides of a square are equal

AB = BC = CD = AD [1]

Also, AOB is an equilateral triangle and all sides of an equilateral triangle are equal

AB = OA = OB [2]

From [1] and [2]

AB = BC = CD = AD = OA = OB [3]

Now,

AD = OA

⇒ ∠AOD = ∠ADO [Angles opposite to equal sides are equal]

In ΔAOD, By angle sum property

∠AOD + ∠ADO + ∠OAD = 180°

⇒ ∠AOD + ∠AOD + (∠CAB - ∠OAB) = 180°

Now, ∠CAB = 90° [Angle in square] and

∠OAB = 60° [Angle in an equilateral triangle]

⇒ 2∠AOD + 90° - 60° = 180°

⇒ 2∠AOD = 150°

⇒ ∠AOD = 75°

Similarly, ∠BOC = 75°

Now,

∠AOD + ∠COD + ∠BOC + ∠AOB = 360°

⇒ 75° + ∠COD + 75° + 60° = 360°

⇒ ∠COD = 150°